Dynamics of one magnetic island in cylindrical compressible plasma S

The full set of the standard resistive massless equations is solved for the nonlinear dynamics of one helical magnetic island in a cylindrical compressible plasma (in the low β tokamak ordering). If δ' > 0 we find a curvature dependent critical island width $\text{x}{}_{\mathrm{\pi }}{}^1\text{α∥ D}{}_{\mathrm{s}}\text{/Δ'∥}$ above which the Rutherford solution is recovered for a tearing mode (D_s and Δ' are respectively the Suydam and FKR(1) factors).     

Hierarchical fermion masses in SU(5)

Rediative masses are generated for the first and the second fermion families by exploiting the idea that their chirality is a symmetry of the “low-energy” SU(3) × SU(2) × U(1) approximation of SU(5), broken only by including the effects of superheavy particles. With only 5's of Higgs coupled to fermions and getting a non-zero vacuum expectation value, we unavoidably get (i) $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{m}{}_{\mathrm{\mu }}\text{3}$ at the grand unification scale; (ii) the charm quark needing a direct mass as the third family; (iii) neutrino masses of size $\text{? (}\text{α}\text{π}\text{)}\text{M}{}_{\mathrm{W}}{}^2\text{M}$.     

A numerical study of the likelihood of phase locking

We report the results of numerical computation of the size of the set of ω's for which the hemeomorphism of the circle $\text{f}\text{?}{}_{\mathrm{K}}$,ω(x)=x+ω+K/2π sin (2πx) mod (1) is phased locked, for values of K ranging from 0.1 to 1. The results suggest that for moderate values of K phase locking is unlikely except for small periods, but that for K=1 almost all ω's give phase locking, with large periods accounting for a surprisingly large portion of the total.     

Magnetic hysteresis studies on slow cooled and quenched CuxZn1−xFe2O4 system

Magnetisation for both slow cooled and quenched samples of Cu_xZn_1?xFe₂O₄ as a function of Zn content has shown a maximum at x = 0.6 and a decrease for x0.6. The increase of magnetisation is explained on the basis of Neel's two sub-lattice model while the decrease of magnetisation is explained on a three sub-lattice model where $\text{r}{}_{\mathrm{ex}}\text{=J}{}_{\mathrm{bb}}\text{S}{}_{\mathrm{b}}\text{/J}{}_{\mathrm{ab}}\text{S}{}_{\mathrm{a}}\text{3}\text{4}$. Quenched samples showed higher magnetisation than the slow cooled ones and this increased with the increase of temperature of quenching. The cation transfer between the two sites, characteristic of the temperature, that can be frozen-in seems to govern this. Variation of M_r/M_s with the content of Zn for both slow cooled and quenched samples indicated more impedence to the domain wall motion or higher Zn content. As the temperature of quenching is increased M_r/M_s decreases and this is attributed to detect cluster formation.     

Meson decays in the non-relativistic quark model

Treating light as well as heavy pseudoscalar and vector mesons as non-relativistic quarkonia, we calculate various decay modes, including lowest QCD corrections. All decay modes studied are in good agreement with experiment, indicating that the quarkonium treatment is applicable to light mesons η, η′, π, also. Consistency of the quarkonium and current algebra treatments for the process π⁰ → 2λ leads to $\text{f}{}_{\mathrm{\pi }}\text{= (}\text{3}\text{2π}\text{)m}{}_{\mathrm{<mtext>u</mtext>}}\text{{1 ? (0.62/4π)α}{}_{\mathrm{<mtext>s</mtext>}}\text{(μ)},}\text{where}\text{m}{}_{\mathrm{<mtext>u</mtext>}}$ is the constituent u-quark mass, and $\text{f}{}_{\mathrm{\pi }}\text{? 93}\text{MeV}$.     

Higher order correction to the sine-Gordon soliton mass

We calculate in the 2-dimensional sine-Gordon theory

$\text{L}{}_{\mathrm{GC}}\text{=}\text{1}\text{2}\text{(?}{}^{\mathrm{\mu }}\text{φ)}{}^2\text{?(}\text{m}{}_4\text{λ}\text{)[1?cos(}\text{λ}\text{φ}\text{m}\text{)]}$

the soliton mass M_sol to order λ and compare it to the meson mass. We find

$\text{M}{}_{\mathrm{sol}}\text{m}{}_{\mathrm{menson}}\text{=}\text{8m}{}^2\text{λ}\text{?}\text{1}\text{π}\text{+}\text{λ}\text{192m}{}^2\text{+O(λ}{}^2\text{)}$

This supports the belief that the field-theoretic WKB approximation of Dashen, Hasslacher and Neveu gives the correct answer for the sine-Gordon problem.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Spectroscopic information on ground-state Ar2, Kr2, and Xe2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar₂, Kr₂, and Xe₂ were obtained from accurate fits to the molecular beam scattering data. From the calculated $\text{Δ}\text{G}{}_{\mathrm{<mtext>v+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{'}\text{s}$ and B_v's, the following spectroscopic constants (in cm^?1) were fitted: for Ar₂ω_e = 31.92, ω_ex_e = 3.31, ω_ey_e = 0.11, B_e = 0.060, α_e = 0.004; for $\text{Kr}{}_2\text{ω}{}_{\mathrm{e}}\text{? 23.99}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 1.30}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.021}$, $\text{B}{}_{\mathrm{e}}\text{? 0.024}$, $\text{α}{}_{\mathrm{e}}\text{? 0.001}$; for $\text{Xe}{}_2\text{ω}{}_{\mathrm{e}}\text{? 21.26}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 0.75}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.008}$, $\text{B}{}_{\mathrm{e}}\text{? 0.013}$, $\text{α}{}_{\mathrm{e}}\text{? 0.0004}$.     

On the physical basis for Urbach's rule

The low-energy tail of the E 6 a exciton in GeS obeys Urbach's rule, with Urbach parameters σ₀ = 1.45 ± 0.05, and $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{= 8.7 ± 0.6 meV}$. The energy ?ω_p corresponds to a previously measured rigid-layer vibrational mode which has no associated electric field. This finding is inconsistent with Dow and Redfield's unified theory of Urbach and exponential absorption edges. Our results are consistent with Sumi and Toyazawa's theory of Urbach edges, and with Fivaz and Mooser's model for electron-phonon interactions in layered compounds.     

The derivative rule for helicity-flip amplitudes

Consequences of the derivative relation $\text{f}{}_{\mathrm{+-}}\text{=}\text{λ?f}{}_{\mathrm{++}}\text{?√?t}$, proposed empirically and also in various models for s-channel helicity amplitudes, are explored. A comparison with π^?p→π⁰n charge-exchange data is made, imposing the usual Regge pole form on f_+-. The assumptions are seen to conflict with the s-dependence of the cross-section dip and the polarization structure. There are also difficulties with finite energy sum rules and with-experimental data on some other reactions.     

Two new Regge trajectories in the Neveu-Schwarz model

The existence of two new families of Regge trajectories at the tree diagram level of the Neveu-Schwarz dual pion model is pointed out. They both have odd G-parity but are of opposite naturality. The highest lying new trajectory is related to the usual unnatural parity pion trajectory $\text{α}{}_{\mathrm{\pi }}\text{by}\text{β}{}_{\mathrm{\pi }}\text{=}\text{1}\text{2}\text{α}{}_{\mathrm{\pi }}\text{+}\text{1}\text{2}$. It factorizes and has positive signature. The parent of the new natural parity trajectories is related to the usual trajectory α_ω by $\text{β}{}_{\mathrm{\omega }}\text{=}\text{1}\text{2}\text{α}{}_{\mathrm{\omega }}$.     

Order relations for lattice sums from order relations for theta functions

Let {τ} and {γ} denote mutually reciprocal unit Bravais lattices in an n-dimensional Euclidean space, and consider the Theta Functions (TF's) $\text{V}{}_{\mathrm{\tau }}\text{(t) = t}{}^{\mathrm{<mtext>n</mtext><mtext>4</mtext>}}\text{∑}{}_{\mathrm{\tau }}\text{exp}\text{(?πtτ}{}^2\text{)}$ for all 0 < t < ∞. By showing how to evaluate a larger class of sums $\text{Z}{}_{\mathrm{\tau }}{}^{\mathrm{(K)}}\text{(t)  π}{}^{\mathrm{k}}\text{t}{}^{\mathrm{<mtext>k\; +\; </mtext><mtext>n</mtext><mtext>4</mtext>}}\text{∑}{}_{\mathrm{\tau }}{}_{\mathrm{r}}{}^{\mathrm{2k}}\text{exp (?πtτ}{}^2\text{)}$, k a nonnegative integer, we are able to evaluate any derivative of the V-functions. With this information we find order relations for the TF's on the cubic lattices in three dimensions. Coupling these relations with Ewald's Theta Function method, we secure order relations for Lennard-Jones, Chaba-Pathria, and other lattice sums on cubic lattices. We also sketch extensions to non-Bravais lattices and give an order relation for TF's on the non-Bravais hexagonal closepacked and the Bravais facecentered cubic.     

Measurement of the isospin amplitude ∣M012∣ in the reaction γn → ϱ0(pπ−) at 7.5 GeV

The cross-channel isospin amplitude $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ is measured in the single reaction γn → ?⁰(pπ^?) at 7.5 GeV assuming the ?⁰ dominance model. A low-mass enhancement is found for $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}{}^2$ in the range of m(pπ^?) of ～1.2 to ～1.7 GeV. The reaction strongly violates s-channel helicity conservation but is consistent with t-channel helicity conservation. The $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ features are found to be very similar to those obtained in previous analyses of πp → π(Nπ) reactions.     

Third order elastic constants and thermal expansion of terbium

The third-order elastic constants and the temperature variation of the effective Grüneisen functions of terbium have been calculated on the basis of Keating's method. The pressure derivatives of the second order elastic constants of terbium have been obtained by interpolation of the experimental pressure derivatives of gadolinium and dysprosium. The ten third order elastic constants of terbium are calculated using four third order anharmonic parameters obtained from its interpolated pressure derivatives. The low and high temperature limits $\text{λ}{}_{\mathrm{L}}$ and $\text{λ}{}_{\mathrm{H}}$ of the lattice thermal expansion are evaluated. The agreement between the calculated $\text{λ}{}_{\mathrm{H}}$ and that obtained from thermal expansion and specific heat data of terbium is good.     

Multiplicities in lepton-hadron processes

The average multiplicity in deep inelastic electro- and neutrinoproduction at large ω(ω～s/Q² + 1) is related in Feynman's version of the parton model to the average multiplicities in high-energy electron-positron annihilation and hadron-hadron scattering. The relation is: , where C_e⁺e^? and C_h are, respectively, the coefficients of ln(s/M_1⊥²) in the multiplicities from e⁺-e^? and P-P in to hadrons, and M_1⊥ is an average transverse mass.     

The ′T Hooft-Polyakov monopole near the Prasad-Sommerfield limit

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit $\text{μ}{}^2\text{2M}{}_{\mathrm{W}}{}^2\text{=}\text{λ}\text{? 1}$, where μ equals the mass of the scalar particle and M_W equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: $\text{γ}$ and λ ln λ. The monopole mass M_m is calculated to order $\text{μ}{}^2\text{M}{}_{\mathrm{W}}$ as

$\text{M}{}_{\mathrm{m}}\text{=}\text{4π}\text{e}{}^2\text{M}{}_{\mathrm{w}}\text{1+}\text{1}\text{2}\text{μ}\text{M}{}_{\mathrm{w}}\text{+}\text{1}\text{2}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}\text{ln}\text{μ}\text{M}{}_{\mathrm{w}}\text{+0.7071}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}$

.     

Theory of donor states in GaP: The role of the camel's back

We present a theoretical study of the influence of the camel's back structure on the low lying excited states of the donors in GaP. Based on comparison with the observed spectrum, we conclude that the appropriate values for the parameters describing the camel's back are $\text{Δ}\text{E}\text{= 3.2}\text{meV and k}{}_{\mathrm{o}}\text{= 0.083 (}\text{a}{}_{\mathrm{o}}\text{2π}\text{)}$.     

Quantum theory of longitudinal dielectric response properties of a two-dimensional plasma in a magnetic field

An analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a two-dimensional thermal Green's function for electron propagation in a magnetic field developed in closed form. The longitudinal-electrostatic plasmon dispersion relation is discussed in the low wavenumber regime with nonlocal corrections, and Bernstein mode structure is studied for arbitrary wavenumber. All regimes of magnetic field strength and statistics are investigated. The class of integrals treated here should have broad applicability in other two-dimensional and finite slab plasma studies.The two-dimensional static shielding law in a magnetic field is analyzed for low wavenumber, and for large distances we find $\text{V(}\text{r}\text{) ～}\text{Q}\text{k}{}_0{}^2\text{r}{}^3$. The inverse screening length $\text{k}{}_0\text{=}\text{2πe}{}^2\text{??}\text{?ξ}$ (? = density, ξ = chemical potential) is evaluated in all regimes of magnetic field strength and all statistical regimes. k₀ exhibits violent DHVA oscillatory behavior in the degenerate zero-temperature case at higher field strengths, and the shielding is complete when $\text{ξ = r′}\text{l}\text{z.shtsls;}\text{ω}$, but there is no shielding when $\text{ξ ≠ r′}\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}$. A careful analysis confirms that there is no shielding at large distances in the degenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> ξ}$. Since shielding does persist in the nondegenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> KT}$, there should be a pronounced change in physical properties that depend on shielding if the system is driven through a high field statistical transition. (It should be noted that the static shielding law of semiclassical and classical models has no dependence on magnetic field in two dimensions, as in three dimensions.) Finally, we find that the zero field two-dimensional Freidel-Kohn “wiggle” static shielding phenomenon is destroyed by the dispersal of the zero field continuum of electron states into the discrete set of Landau-quantized orbitals due to the imposition of the magnetic field.     

A mathematical interpretation of Dirac's formalism part a: Dirac bases in trajectory spaces

In this paper the notion of Dirac basis will be introduced. It is the continuous pendant of the discrete basis for Hilbert spaces. The introduction of this new notion is closely related to the theory of generalized functions. Here De Graaf's theory will be employed. It is based on the triplet $\text{S}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}\text{?X?}\text{T}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}$ where X is a Hilbert space. In a well specified way any member of $\text{T}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}$ can be expanded with respect to a Dirac basis. Both the introduction of Dirac bases and a new interpretation of Dirac's bracket notion will lead to a mathematical rigorization of various aspects of Dirac's formalism for quantum mechanics. This rigorization goes much beyond earlier proposals.